Linear Filtering of Bivariate Signals Using Quaternions

A new approach towards linear time-invariant (LTI) filtering of bivariate signals is proposed using a tailored quaternion Fourier transform. In the proposed framework LTI filters are naturally described by their eigenproperties providing economical, physically interpretable and straightforward filtering definitions in the frequency domain. It enables an easy design of LTI filters and a simple method for spectral synthesis of bivariate signals with prescribed frequency polarization properties. It also yields various natural decompositions of bivariate signals. Numerical experiments illustrate the approach.